Treffer: Statistical implicative analysis of students' algebra performance

The data mining method of Statistical Implicative Analysis is used to reveal details of the inner structure of algebraic competence as seen in data collected from beginning algebra students as part of the development of the SMART online diagnostic tests. The implicative analysis of the data shows the logical relation between algebraic sub-competencies. This paper reports item level analysis, comparing different cut-off levels for implication intensity, and a follow-up analysis of scales constructed from the clusters revealed. Finally in a novel application of statistical implicative analysis, the paper identifies pairs of scales that together imply an outcome, but do not do so separately. This allows the identification of abilities that are necessary foundations for other parts of algebraic proficiency.